Page 1: This is not timed, however questions 2-4 are about fluency, so students should be able to answer these questions without counting or drawing. Question 1 is a conceptual question to check students’ understanding of multiplication. Page 2: The first set of multiplications is timed. Ask students to work from left to right across a row, then go to the next row, rather than going down each column. At the end of one minute, ask students to circle the problem they just finished. Then give them an additional 30 seconds to finish any that are left. There are two purposes to this assessment: 1) Can students recite multiplications quickly and accurately, without counting (the definition of fluency) and 2) Which particular combinations do individual students still need to work on. When you score the paper, circle the ones that are wrong and ask them to list each of those on a separate paper, and figure out the right answer. (Handout 4: Multiplication fact families I need to learn.)
The rest of page two gives you insight into whether they can use knowledge of multiplication and division relationships to find related quotients.
Page 3: This second set of multiplications is timed, like the first set. Again, ask students to work from left to right across a row, then go to the next row, rather than going down each column. At the end of one minute, ask students to circle the problem they just finished. Then give them an additional 30 seconds to finish any that are left.
Question 8 gives you insight into students’ understanding of remainders. Question 9 is a place value item.
Memorizing "facts": There are some multiplication fact families that aren't easily computed through strategies. Most often we need to simply spend some time memorizing those. They include most of the squares, although students tend to remember those more easily, many of the 3's (although many students learn those through skip counting at an early age) and many of the 7's and 8's. Students who are good at memorizing might find this the easiest way to learn the combinations. But remember that many students are not good at memorizing, so it's OK for them to rely on strategies until the combinations become automatic. (For example, a child who is having trouble with 7x6 might know 6x6 and then add 6 more by counting up. A strategy that relies on counting is not very efficient, so they need to be encouraged to move from this strategy to remembering the fact. Try additional strategies like this: 6x6 is 36, then 6 more... 4 more is 40, and 2 more is 42. They can do this quickly, without actually counting each number from 36 to 42.)
Multiplication Concepts
Students who know very few multiplication/division fact families might be struggling with the basic concepts of multiplication and division. Use this assessment (Handout 6: Multiplication and division concepts) to determine what they know about the basic concepts, then design an appropriate teaching approach to help them learn. The teaching approach should include the use of Well-structured problems (teacher background paper).
Fluency Games
Students have fun practicing their fact families with games, like the ones below (much more fun than using flash cards). Fluency develops as students use strategies more and more quickly in friendly competition.
Flip card multiplication
Two students play this card game, sitting across from each other. Each student has half of the deck of cards, which they hold face down. They each turn one card up and put it on the table at the same time, then the first person who says the product of the two cards gets those cards. (Face cards count as 10.)
The play continues until one player has all the cards.
Be careful how you match kids up, or the game ends quickly!
Four students play this game, taking turns. The player whose turn it is rolls two dice – one is a standard die with 1-6, the other is a number cube marked with 3-8. They then mark off the space on their game board that corresponds to the product (the game board is published in Teaching Learners Who Struggle with Mathematics: Systematic Intervention and Remediation (2nd Edition), by Sherman, Richardson and Yard, published by Prentice Hall, 2008 - buy this book: It has very valuable approaches for helping struggling learners).
The first person to mark out all facts on his or her side of the board is the winner.
If another student thinks the player’s product is wrong, he or she can challenge. If the challenging player wins, they can mark off any additional product on their board.
The game can be played with two number cubes marked 4-9 for more challenge. Create your own game board for this.
Start by using this assessment: Handout 3: Multiplication and division fluency assessment
Page 1: This is not timed, however questions 2-4 are about fluency, so students should be able to answer these questions without counting or drawing. Question 1 is a conceptual question to check students’ understanding of multiplication.
Page 2: The first set of multiplications is timed. Ask students to work from left to right across a row, then go to the next row, rather than going down each column. At the end of one minute, ask students to circle the problem they just finished. Then give them an additional 30 seconds to finish any that are left. There are two purposes to this assessment: 1) Can students recite multiplications quickly and accurately, without counting (the definition of fluency) and 2) Which particular combinations do individual students still need to work on. When you score the paper, circle the ones that are wrong and ask them to list each of those on a separate paper, and figure out the right answer. (Handout 4: Multiplication fact families I need to learn.)
The rest of page two gives you insight into whether they can use knowledge of multiplication and division relationships to find related quotients.
Page 3: This second set of multiplications is timed, like the first set. Again, ask students to work from left to right across a row, then go to the next row, rather than going down each column. At the end of one minute, ask students to circle the problem they just finished. Then give them an additional 30 seconds to finish any that are left.
Question 8 gives you insight into students’ understanding of remainders. Question 9 is a place value item.
Strategies for Multiplication
When each student knows the fact families that are still hard for them to remember, use Handout 5: Strategies for multiplying, to teach students in small groups who need to learn particular combinations. Also see this nice website: http://naturalmath.com/mult/mult13.html
Memorizing "facts": There are some multiplication fact families that aren't easily computed through strategies. Most often we need to simply spend some time memorizing those. They include most of the squares, although students tend to remember those more easily, many of the 3's (although many students learn those through skip counting at an early age) and many of the 7's and 8's. Students who are good at memorizing might find this the easiest way to learn the combinations. But remember that many students are not good at memorizing, so it's OK for them to rely on strategies until the combinations become automatic. (For example, a child who is having trouble with 7x6 might know 6x6 and then add 6 more by counting up. A strategy that relies on counting is not very efficient, so they need to be encouraged to move from this strategy to remembering the fact. Try additional strategies like this: 6x6 is 36, then 6 more... 4 more is 40, and 2 more is 42. They can do this quickly, without actually counting each number from 36 to 42.)
Multiplication Concepts
Students who know very few multiplication/division fact families might be struggling with the basic concepts of multiplication and division. Use this assessment (Handout 6: Multiplication and division concepts) to determine what they know about the basic concepts, then design an appropriate teaching approach to help them learn. The teaching approach should include the use of Well-structured problems (teacher background paper).
Fluency Games
Students have fun practicing their fact families with games, like the ones below (much more fun than using flash cards). Fluency develops as students use strategies more and more quickly in friendly competition.
Flip card multiplication
Two students play this card game, sitting across from each other. Each student has half of the deck of cards, which they hold face down. They each turn one card up and put it on the table at the same time, then the first person who says the product of the two cards gets those cards. (Face cards count as 10.)
The play continues until one player has all the cards.
Be careful how you match kids up, or the game ends quickly!
The Product Game and Factor Game
Two good online practice games:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=29
http://illuminations.nctm.org/ActivityDetail.aspx?ID=64
You can make a board game out of the Product Game if getting online is not easy.
Rollette
Four students play this game, taking turns. The player whose turn it is rolls two dice – one is a standard die with 1-6, the other is a number cube marked with 3-8. They then mark off the space on their game board that corresponds to the product (the game board is published in
Teaching Learners Who Struggle with Mathematics: Systematic Intervention and Remediation (2nd Edition), by Sherman, Richardson and Yard, published by Prentice Hall, 2008 - buy this book: It has very valuable approaches for helping struggling learners).
The first person to mark out all facts on his or her side of the board is the winner.
If another student thinks the player’s product is wrong, he or she can challenge. If the challenging player wins, they can mark off any additional product on their board.
The game can be played with two number cubes marked 4-9 for more challenge. Create your own game board for this.